# integralBoxFilter

2-D box filtering of integral images

## Description

B = integralBoxFilter(A) filters the integral image A with a 3-by-3 box filter. Returns the filtered image, B.

example

B = integralBoxFilter(A,filterSize) filters the integral image A with a 2-D box filter with size specified by filterSize.

B = integralBoxFilter(___,Name,Value) uses name-value pairs to control various aspects of the filtering.

## Examples

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Pad the image by the radius of the filter neighborhood. This example uses an 11-by-11 filter.

filterSize = [11 11];

Compute the integral image of the padded input image.

Filter the integral image.

B = integralBoxFilter(intA, filterSize);

Display original image and filtered image.

figure
imshow(A)
title('Original Image')

figure
imshow(B,[])
title('Filtered Image')

Calculate the integral image of the padded input.

Filter the integral image with a vertical [11 1] filter.

Bvert = integralBoxFilter(intA, [11 1]);

Crop the output to retain input image size and display it.

Bvert = Bvert(:,6:end-5);

Filter the integral image with a horizontal [1 11] filter.

Bhorz = integralBoxFilter(intA, [1 11]);

Crop the output to retain input image size.

Bhorz = Bhorz(6:end-5,:);

Display the original image and the filtered images.

figure,
imshow(A)
title('Original Image')

figure,
imshow(Bvert,[])
title('Filtered with Vertical Filter')

figure,
imshow(Bhorz,[])
title('Filtered with Horizontal Filter')

## Input Arguments

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Integral image to be filtered, specified as a numeric array of any dimension.

The integral image must be upright — integralBoxFilter does not support rotated integral images. The first row and column of the integral image is assumed to be zero-padded, as returned by integralImage.

Data Types: double

Size of box filter, specified as a positive, odd integer or 2-element vector of positive, odd integers. If filterSize is scalar, then integralBoxFilter uses a square box filter.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

### Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: B = integralBoxFilter(A,5,'NormalizationFactor',1);

Normalization factor applied to box filter, specified as a numeric scalar.

The default 'NormalizationFactor' has the effect of a mean filter — the pixels in the output image are the local means of the image. To get local area sums, set 'NormalizationFactor' to 1. To avoid overflow in such circumstances, consider using double precision images by converting the input image to class double.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

## Output Arguments

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Filtered image, returned as a numeric array. integralBoxFilter returns only the parts of the filtering that are computed without padding.

Data Types: double

## Version History

Introduced in R2015b